ARITHMETIC OPERATIONS OF GENERALIZED PICTURE FUZZY NUMBERS BY (α, γ, β) – CUT METHOD

Picture fuzzy set is an extension of intuitionistic fuzzy set and fuzzy set and it is capable to analyze the uncertain and vague information more effectively. It is applicable in situations where human decisions claim more variety of responses like yes, no, abstain and refusal which cannot be addressed in the traditional fuzzy set and intuitionistic fuzzy set. In this article, the arithmetic operations such as scalar multiplication of a generalized trapezoidal and triangular picture fuzzy numbers and the division and multiplication of two generalized trapezoidal and triangular picture fuzzy numbers by (α, γ, β) – cut method are discussed thoroughly. Finally, some numerical examples are described to illustrate the proposed operations.